Digital subscriber line (DSL) technologies can provide large bandwidth for digital communications over existing subscriber lines. When transmitting data over the subscriber lines, crosstalk interference can occur between the transmitted signals over adjacent twisted-pair phone lines, for example in a same or nearby bundle of lines. Crosstalk introduces noise in DSL systems and reduces the data-rates that can be achieved in the DSL systems. Thus, crosstalk can significantly limit the performance of DSL technologies that use higher frequency bands, such as very high bit rate DSL 2 (VDSL2). Crosstalk can be canceled or reduced by joint processing or precoding of downstream signals in multiple subscriber lines that may be bundled, e.g. in a binder, at the network end. Crosstalk precoding is a technique in which signals from a set of signals at the network central office (CO) are pre-distorted prior to transmission through the binder. A pre-distortion filter or ‘precoding matrix’ is used to pre-distort the signals, and thus cancel crosstalk that occurs between the lines in the binder. The signals may then arrive at the receivers at different customer sites substantially free of crosstalk, thereby achieving significantly higher data-rates.
A crosstalk precoder can be used in a modem, e.g. at the CO, to eliminate or reduce crosstalk in the subscriber lines. The crosstalk precoder uses precoding coefficients, e.g. in a precoding matrix, to modify the signals in the lines and transmits the pre-distorted signals downstream from the CO to a plurality of customer premise equipments (CPEs). The introduced pre-distortions in the signals substantially cancel the crosstalk in the signals that are received by the CPEs. The crosstalk precoder is trained or initialized using feedback signals from the CPEs, which indicate the errors in the received signals at the CPEs. To train the crosstalk precoder, a VDSL transceiver office unit (VTU-O) at the CO sends a sequence of pilot symbols downstream to a VDSL transceiver remote unit (VTU-R) at a CPE, which returns corresponding error feedback signals to a Vectoring Control Entity (VCE) coupled to the VTU-O and the crosstalk precoder. The error feedback signals from the CPEs are then used to update the precoding matrix coefficients and thus adjust the pre-distorted signals until reaching convergence.